How to Compare Different Loss Functions and Their Risks

By Ingo Steinwart. 2007

203 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability, Optimization & Training, Evaluation & Benchmarks

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Citations in the corpus

Quantifying Learning Guarantees for Convex but Inconsistent Surrogates (2018, background): “Consistency of convex surrogates has been the central question of many studies for such problems as binary classification [2, 24, 19], multi-class classification [23, 21, 1, 17], ranking [11, 4, 5, 18, 15] and, more recently, structured prediction [7, 14].”
On Structured Prediction Theory with Calibrated Convex Surrogate Losses (2017, methodology): “Ávila Pires et al. [2] generalize the theoretical framework developed by Steinwart [39] and present results for the multi-class SVM of Lee et al. [23] (the score vectors are constrained to sum to zero) that can be built for any task loss of interest.”
An Explanation of In-context Learning as Implicit Bayesian Inference (2021, background): “Then for k ≥ 2 and as n → ∞ , the 0-1 risk of the in-context learning predictor f n is bounded as where (Steinwart, 2007, Ávila Pires and Szepesvári, 2016) for the multiclass logistic loss for δ ∈ [0 , 1) , assuming that the minimizers of the 0-1 risk and multiclass logistic risk are the same.”
Calibrated asymmetric surrogate losses (2012, methodology): “13 of Steinwart [31] and surrounding discussion.”
Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings (2015, background): “…have been investigated independently for quite some time (see for example Bartlett et al. (2006), Tewari and Bartlett (2005), Zhang (2004), Steinwart (2007), Reid and Williamson (2011), Calauzènes et al. (2012, 2013), Scott (2012), Duchi et al. (2013), Menon and Williamson (2014),…”
Convex Calibration Dimension for Multiclass Loss Matrices (2014, background): “More recently, Pires et al. [20] used Steinwart’s techniques to obtain surrogate regret bounds for certain surrogates w.r.t. general multiclass losses, and Ramaswamy et al. [22] showed how to design explicit convex calibrated surrogates for any low-rank loss matrix.”
Convex Calibrated Surrogates for Low-Rank Loss Matrices with Applications to Subset Ranking Losses (2013, background): “There has been much interest in recent years in understanding consistency properties of learning algorithms – particularly algorithms that minimize a surrogate loss – for a variety of finite-output learning problems, including binary classification, multiclass classification, multi-label classificat”
Consistent Multiclass Algorithms for Complex Performance Measures (2015, background): “, 2012), and some work on general multiclass losses (Steinwart, 2007; Ramaswamy & Agarwal, 2012; Pires et al., 2013; Ramaswamy et al., 2013).”
"On the (Non-)existence of Convex, Calibrated Surrogate Losses for Ranking" (2012, methodology): “We present in this section the notion of calibration as studied in [20], which is the basis of our work.”
Cross-Entropy Loss Functions: Theoretical Analysis and Applications (2023, background): “, h(x,n), y), for some function Ψ, then it is not hard to show that the minimizability gap vanishes for the family of all measurable functions: M(Hall) = 0 (Steinwart, 2007)[lemma 2.”